Effect of noise on recovery. In this experiment, we study the performance of single-graph demixing (REF ) with \(\text{L}=3\) , varying \(\text{R}\)  and \(\text{S}\) , and in the presence of additive white Gaussian noise \(\mathcal {N}(0,\sigma _n^2)\)  (see remark:robustdemixing for a discussion on handling noisy observations). The graph at hand corresponds to the adjacency matrix of Zachary's karate club network [1]}, which contains \(\text{N}=34\)  nodes (the members of the club) and 78 undirected edges (symbolizing friendships among members). The results reported in Fig:singlegraphkarate reveal that, in all cases, the demixing error decreases as \(\sigma _n\)  decreases and it increases as either \(\text{R}\)  or \(\text{S}\)  increase. Furthermore, if the value \(\text{R}+\text{S}\)  is fixed, successful demixing is easier for smaller values of \(\text{R}\) . Once again, this suggests that the sensitivity of the demixing performance with respect to \(\text{R}\)  is larger than that for \(\text{S}\) .
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